1549055259-Ubiquitous_Quasidisk__The__Gehring_

170

of order a , 79
harmonic bending (property), 46, 46 ,
149-152
harmonic doubling condition, 83
harmonic measure, 42
harmonic quasisymmetry (property), see
quasisymmetric domain
Hayman, W. K., 40 , 52 , 122
Hayman-Wu theorem, see level-set
inequality
Heinonen, J ., 4, 11 , 46, 51, 52 , 109 , 151
Herron, D., 24
Hjelle, G. A., 91 , 92
homogeneous (set), 91
homogeneous with respect to QC(K), 91,
153
hyperbolic
density, 34
distance, 34
line, 34
metric, 22, 34-38, 138-148
segment, 34
hyperbolic segment property, 39, 101 , 104
injectivity criteria, 59
iterate, 16
lwaniec, T., 3, 11 , 109
J1, 5
fo, 35, 35 - 38, 87 , 138-144
Jacobian, 5
of K-quasiconformal mapping, 67
of locally K-quasiconformal mapping, 67
Jerison, D. E., 84 , 100
John disk, 77 , 78
John, F. , 63, 69, 127, 129 , 130
Jones, P. W., 38, 52, 71, 73, 138 , 139
Julia set, 16
Junge, S., 84
K-quasiconformal, 4
K-quasiconformal (in Rn), 94
K-quasiconformally decomposable, 31
K-quasidisk, 12
K , 47
Kallunki, S., 4
Kaufman, R., 79, 81
Kelingos, J. A., 109
Kenig, C. E., 84 , 100
Kerekjart6's theorem, 123
Kim, K., 84, 92
Koskela, P., 4
Krzyz, J. G., 45
Kiihnau, R., 21
L(D), 63, 130, 134
L(G), 90
L1(x,r) (in Rn), 94
L1(z,r), 3

INDEX

Lip"'-extension domain, 81

Lip"'(D), 78

locLip"'(D), 7 8, 81

l1(x,r) (in Rn), 94

l1(z,r), 3

Ly(D), 71

Ly-extension domain, 72

.>-(r), 6

Langmeyer, N ., 28, 84 , 88

Lappalainen, V ., 79, 81 , 82

Latfullin, T. G., 72

Lehtinen, M., 60 , 62

Lehto, 0 ., 3- 6, 11, 48-50, 60, 62 , 73, 109 ,

110, 146 , 156, 158

level-set inequality, 52

limit set, 90

linear local connectivity, 27

linearly connected domain, 77

linearly locally connected, 27, 28-30, 95,

104, 106 , 123 , 126, 132-135, 161

Lipschitz class, 78

local, 78 , 81

Littlewood, J. E. , 78

Liu, X., 87

locally K-quasiconformal mapping, 64

locally L-bilipschitz mapping, 62

Lusin's property (N), 5, 15

Luukkainen, J., 24

m (Lebesgue measure), 5

mod(r), 6

μ , 50

μv, 50

μf, 5

Marshall, D. E., 43 , 52, 84

Martin, G., 3, 11, 109

Martio, 0., 39 , 40, 51 , 52, 63, 64, 77,

79 - 83, 118 , 123, 130, 159

Maskit, B ., 90

Mattila, P., 15

McMillan, J. E., 150

measurable Riemann mapping theorem, 6

Menchoff, D., 3

meromorphic function, 16, 59

Miller, J., 21

Miller-Van Wieren, L ., 62

min-max property (geodesic), 42, 134, 135

Minda, D., 87

modulus

of curve family, 6, 47

of quadrilateral, 46

Morrey, C. B., 6

Moser, J., 69

Nakki, R., 77, 78

Nehari, Z., 60

Nevanlinna, R., 127, 129, 150